Linearization of fourth-order ordinary differential equations by point transformations

TL;DR

This paper characterizes all fourth-order ODEs linearizable via point transformations, providing a test and method for deriving the linearizing transformations and equations.

Contribution

It identifies the class of linearizable fourth-order equations and offers a systematic procedure for their linearization.

Findings

All linearizable fourth-order equations are linear in the third derivative.

A linearization test for these equations is developed.

A method for obtaining linearizing transformations is described.

Abstract

We present here the solution of the problem on linearization of fourth-order equations by means of point transformations. We show that all fourth-order equations that are linearizable by point transformations are contained in the class of equations which is linear in the third-order derivative. We provide the linearization test and describe the procedure for obtaining the linearizing transformations as well as the linearized equation.